A346133 Numbers N = A * B such that N (reversed digits) = A (reversed digits) * B (reversed digits). A single-digit number is its own reversal and neither A nor B has a leading zero. No pair (A, B) has both A and B palindromic or simple-digit. The reversed products are not included in the sequence.

24, 26, 28, 36, 39, 46, 48, 68, 69, 132, 143, 144, 154, 156, 165, 168, 169, 176, 187, 198, 204, 206, 208, 224, 226, 228, 244, 246, 248, 252, 253, 264, 266, 268, 273, 275, 276, 284, 286, 288, 294, 297, 299, 306, 309, 336, 339, 366, 369, 374, 384, 385, 396, 399

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(1) = 24 = 2 * 12 and 2 * 21 = 42 (which is 24 reversed);
a(2) = 26 = 2 * 13 and 2 * 31 = 62 (which is 26 reversed);
a(3) = 28 = 2 * 14 and 2 * 41 = 82 (which is 28 reversed);
a(4) = 36 = 3 * 12 and 3 * 21 = 63 (which is 36 reversed); etc.

Mathematica

q[n_] := IntegerReverse[n] >= n && AnyTrue[Rest @ Take[(d = Divisors[n]), Ceiling[Length[d]/2]], (# > 9 || n/# > 9) && !Divisible[#, 10] && !Divisible[n/#, 10] && (!PalindromeQ[#] || !PalindromeQ[n/#]) && IntegerReverse[#] * IntegerReverse[n/#] == IntegerReverse[n] &]; Select[Range[2, 400], q] (* Amiram Eldar, Jul 07 2021 *)

Prog

(Python)
from sympy import divisors
def rev(n): return int(str(n)[::-1])
def ok(n):
    divs = divisors(n)
    for a in divs[1:(len(divs)+1)//2]:
        b = n // a
        reva, revb, revn = rev(a), rev(b), rev(n)
        if revn < n or a%10 == 0 or b%10 == 0: continue
        if (reva != a or revb != b) and revn == reva * revb: return True
    return False
print(list(filter(ok, range(400)))) # Michael S. Branicky, Jul 06 2021

Crossrefs

Cf. A066531.

Sequence in context: A241042 A346290 A097376 * A079720 A053680 A260251

Adjacent sequences: A346130 A346131 A346132 * A346134 A346135 A346136

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jul 05 2021

Status

approved